Abstract: This will be a basic introduction to the finite element method. The finite element method is a method for finding a piece-wise polynomial approximation of the solution to a partial differential equation (PDE).
The goal of this chalk talk will be to provide a preliminary understanding of the finite element method and how we use it to approximate the solution of a PDE by simply solving a sparse linear system. We will then discuss the rigorous mathematical framework of finite element analysis and the mathematically guaranteed accuracy of finite element solutions. Time permitting, we will end the talk with a brief comparison between the classical finite element method and popular machine-learning-based models.
Please note that this talk will be “introductory.” We will not go through lengthy proofs for the sake of time, and no background in PDE theory or Sobolev spaces is required.
See all upcoming talks at https://www.anl.gov/mcs/lans-seminars.